Probing disordered substrates by imaging the adsorbate in its fluid phase

Several recent imaging experiments access the equilibrium density profiles of a monolayer of interacting particles confined to a two-dimensional substrate. When these particles are in a fluid phase, we show that such data yields precise information regarding substrate disorder as reflected in one-point functions and two-point correlations of the fluid. Using Monte Carlo simulations and replica generalizations of liquid state theories, we extract unusual two-point correlations of time-averaged density inhomogeneities induced by disorder. Correlation functions such as these have not hitherto been measured but should be experimentally accessible.